The Chip Zdarsky run is kicked off when Penguin decides that he's sick of the crime life and of fighting Batman, so he fakes his death and leaves Gotham to try and enjoy long overdue retirement. Unfortunately for everyone, he does this by framing Batman for his murder as a final "fuck you" to his nemesis before he departs, which ends up causing the erroneous activation of Failsafe, a robotic weapon that Batman developed years ago meant to take him down on the off-chance that he ever turned evil, and Failsafe proceeds to go on a warpath against Batman that threatens to destroy Gotham in the crossfire.
Crisis on Infinite Earths: Krona got the ball rolling when he first attempted to look at the dawn of the universe, but it's the man who'd become Pariah who kick-starts the plot proper. Having made his world a utopia, he decided to try and find out the origins of the universe, despite everyone telling him not to. He ignores them. His attempt outright destroys his entire universe by accident... and the resulting imbalance proves enough to wake the Anti-Monitor from his eons long slumber, whereupon he starts destroy every universe ever. (Needless to say, some of the survivors are just a little pissed when they learn this fact.)
In The Flash, the Allens come to a doctor to deliver their twins, the same time as the Thawnes are expecting a delivery as well. The Thawne child died in childbirth, and, out of guilt, the doctor gave one of the Allen twins to the Thawnes while fabricating a lie to his real parents that he died. Malcolm "Thawne" grows up in a dysfunctional, criminal family, and when he learns of his true parentage, comes to resent his twin brother Barry as a result. While Barry successfully heads a mostly-familial legacy of superheroes, Malcolm would become the ancestor to multiple supervillains (the second Reverse Flash, Captain Boomerang II, Inertia, not to mention multiple other descendants that bear Malcolm's "Cobalt Blue" villain moniker), creating one of the largest Feuding Families in the DCU.
Green Lantern: The Guardians of the Universe have gradually been flanderized into one entire race of walking disasters:
One member of their race, Krona, attempting to settle the Origin Question (basically, why is there a universe and why is there life in it and specifically why are there Oans/Malthusians in it), introduced Evil (or at least Entropy) into the universe. Later retcons change it so that he instead splintered the universe into the multiverse, unleashed the Anti-Monitor and dragged Volthoom to Oa.
To combat evil, they formed a corps of robotic police called the Manhunters. That didn't work out so well when Krona decided to prove they were fallible by engineering their insanity and set them loose to massacre Sector 666.
To combat evil, the Manhunters, andregulate the Green Lantern Corps, they created the Alpha Lanterns, which were supposed to combine the ruthless efficiency of the Manhunters with a Green Lantern's flexibility. To no one's surprise, the Manhunter programming screwed with the Lanterns' thoughts, turning them into Lawful Stupid parodies of the people they were. And to boot, the process rendered them vulnerable to Demonic Possession.
In The Multiversity, Ultra Comics is exploited by the Gentry as a means to infiltrate the multiverse. While he manages to seal Earth-33 off from them, he's ultimately unsuccessful in defeating the villains. Toward the end, it turns out merely saying the words "S.O.S." summons the Gentry into the universe of whoever says it. So anyone who says it serves as one of these.
Supergirl storyline "Supergirl's Big Brother": Soldier Jan Danvers naively told one man whom he had just befriended, and who looked right like him, about his family and his inheritance, even showing him his locket where he kept his parents' pictures. When Jan dies in battle, his new friend steals his locket and tries to impersonate him, causing Jan's parents greater grief and jeopardizing Supergirl's secret identity.
In The Living Legends of Superman, a defense robot watching over a mining outpost located at the rim of the universe mistakes a meteor shower for an enemy raid and shoots a barrage of atom particle destroyers. The APD missiles explode too near the edge of the universe, tearing a rift in the fabric of time and space which starts destroying the cosmos.
The Phantom Superboy: One nosy lizard steps on the Phantom Zone Projector's switch, accidentally sending Superboy into the Zone. Since nobody else knew about the Zone, Clark could have become trapped forever.
